most recent 30 from http://mathoverflow.net 2013-05-21T13:59:32Z http://mathoverflow.net/feeds/user/13235 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/12211/applications-of-infinite-ramseys-theorem-on-n/56629#56629 Chris 2011-02-25T13:20:02Z 2011-02-25T13:20:02Z

<p>There are, in fact, very deep uses of Ramsey-theoretic methods in analysis. As I recall, Gowers won a Fields medal for using this connection to answer most of the open conjectures about Banach space geometry. For example, he used these methods to show that there exists a Banach space with no unconditional Schauder basis. For a nice (though somewhat advanced) survey, there is a book "Ramsey Methods in Analysis" by Argyos and Todorcevic.</p>